String Theory Demystified

CHAPTER 4
String Quantization
At this point we have the classical physics of the string in place. The next step
toward a quantum theory is, of course, to quantize the string. We will start off by
looking at a quantum theory of a single string. From quantum fi eld theory you recall
that this procedure is known as fi rst quantization. This is opposed to the procedure
called second quantization, which is a viewpoint of quantizing fi elds (see Quantum
Field Theory Demystifi ed for a review). The difference in the two approaches will
be on how we view the X m (s, t ). If we take them to be fi elds, then the quantization
procedure is second quantization. If we take them to be space-time coordinates, as
we have so far, then the process is fi rst quantization. This is the procedure we will
apply in this chapter. There are several different approaches to quantization of the
string, each with their own accompanying diffi culties and problems. The main
approaches used are called covariant quantization, light-cone quantization, and
BRST quantization. We consider the fi rst two approaches here, and will discuss
BRST quantization later.
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